Aptitude - Problems on Trains - Discussion

Why multiply 50/3*18/5 in the last?

Speed= d/t (100+100)=200*18/5=90km/h two train speed x+2x =3x 3x=90; x=90/3 x=30 so faster train speed is 2x =60

SOLVING WITHOUT x

{(100+100)/8}*{(18/5)}=90K/H
NOW,
SPEED=2:1
SO,
90*2/3=60K/H

Actually,
if speed of the slower train be x m/sec.

Then, speed of the faster train y = 2x m/sec=> x=y/2

Relative speed =(x+y)= (y/2+ y) m/sec = 3y/2 m/sec.

(100 + 100)/8 = 3y/2
3y=50
y=50/3 m/s
y=(50/3)*(18/5)kmph

speed of the faster train = 60 kmph

Give me short cut.

When the train is Opposite direction, than the relative speed is add to both (100+100)= 200

In this problem how we can take 50/3?

Now study the problem carefully the given data is
two trains moving in opposite direction . that means we add them 100+100=200mts

to cross these 200mts it takes 8 secs ok
now, they have asked to find the speed of the faster train if the speed is twice the slower train , this is given in the question.

Now ,

speed=distance/time

speed=200mts/8secs ok
as options are given in km/hr , we have to convert speed to km/hr

So we multiply with 18/5
well (200mts/8secs)*18/5=(200/8)*(18/5)=90km/hr
these is the total speed .

Now they asked us to find the speed of the train twice the other train

Let the speed of first train =xkm/hr

Speed of other train should be twice=2x km/hr

So we have got total speed as 90km/hr
x+2x=90km/hr
3x=90km/hr
x=30km/hr
speed of one train is 30km/hr.

So they asked twice the speed of train

So we get 2x=2*30
=60km/hr
Now if we add 30+60=90km/hr

We got the total speed

The speed of the faster train is 60 km/hr

I don't understand please explain it brief.

I didn't understood how can I clear this problem?